Asteroid Collisions: Estimating Their Probabilities and Velocity Distributions

Abstract

A new method of estimating the collisional probabilities and velocities of asteroids is elaborated, differing substantially from previous methods. It is argued that the distance from a target asteroid to the nearest asteroid of an ambient population must be distributed over time according to the Weibull distribution. An empirical distribution of such distances may be generated efficiently by a novel type of computer simulation of the long-term statistical mechanics of large sets of asteroids, a simulation entailing no orbit propagation. The simulation yields distributions of both minimum distances and relative velocity vectors. By estimating the two parameters of this distribution and the mean relative velocity, it is possible to estimate the intrinsic collisional probability of the target asteroid with the ambient asteroid population. The distribution of relative velocities can be estimated directly from the simulation data. Some initial results determined by the new method are, for the mean intrinsic collisional probabilities of 243 Ida, 2 Pallas, and 951 Gaspra with ambient asteroid populations numbering 799, 680, and 533, respectively: 5.34 × 10−18, 5.96 × 10−18, and 2.28 × 10−18km−2year−1. The new method affords an alternative pathway for solving problems in asteroid interactions, a pathway that is fundamentally statistical in nature. It is easy to implement and offers a great deal of flexibility in its basic simulation for quantitatively studying many aspects of collisions and near-collisions involving asteroids, planets, and comets.